of course it can saturate
https://www.allaboutcircuits.com/textbook/semiconductors/chpt-4/common-collector-amplifier/
https://www.electronics-tutorials.ws/amplifier/amp_2.html
A common emitter amplifier yes, it can saturate, but a common collector amplifier can't saturate, unless the input voltage is taken beyond the supply voltage. The tutorial you've linked to actually explains this.
Given the voltage polarities across the base-emitter PN junction and the load resistor, we see that these must add together to equal the input voltage, in accordance with Kirchhoff’s Voltage Law. In other words, the load voltage will always be about 0.7 volts less than the input voltage for all conditions where the transistor is conducting. Cutoff occurs at input voltages below 0.7 volts, and saturation at input voltages in excess of battery (supply) voltage plus 0.7 volts.
In the circuit posted at the start of the thread, the input voltage can't exceed the supply voltage, so the output state can't saturate.
get yourself a real amplifier, put it on your basement and put it to over 80% for a while with nominal load (cut the cooler fan to do it quickly), buy a multimeter or scope and tell us the result
I seems like you're confusing clipping distortion and overheating with saturation of a BJT. If an emitter follower output stage is over-driven, it will clip, distort and possibly overheat, if the heat-sinking and power rating of the transistors is insufficient, but neither of the transistors will ever enter the saturation region. They will both be operating in the active region the entire time.
In any case, adding base resistors to 2SC52EE and 2SA1943 will do little to protect them against overheating. It may improve the stability, at the expense of a reduced voltage swing.
EDIT:
Look here and try to understand in practice it can arrive this situation"The bias resistor must connect to a voltage that is at least 0.7V higher than the supply voltage for the upper emitter-follower transistor to saturate." (eg if you have voltage loss at high power on your wires inside the amplificator, yes, the wires between the final transistor and the +Vdd, I seen this in a clone philips schematic, in practice) :
Sorry, I missed this.
The wires between the final transistor and the supply voltage would have to be a very high resistance, or carrying a large current to drop nearly 1V (more more than 0.7V is required to saturate a transistor). An additional circuit would be required to protect against the high current scenario, as without it the amplifier would be toast anyway.
I see what you mean now and agree: a base resistor would protect against a high resistance or open circuit collector connection, because the maximum base current rating would be exceeded. Are you sure the extra resistor in the Philips amplifier wasn't to improve the stability?
There will be plenty of other points in the amplifier which can be destroyed by a bad connection. For example, what will happen if the connection to one of the zener diodes is bad? The TL071 will get 40V on one of its supply rails.
It's not feasible to protect against everything that can possibly go wrong!